You are here:

Question
Let vector v=[2,-1,1,3], x=[-1,2,-1,-1], y=[0,0,2,1], z=[1,1,2,3]

Are these vectors linearly independent?

If not, give one nontrivial solution of the corresponding system of linear equation,and write  one dependency equation

Questioner:   Michelle
Private:   Yes  <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<< changed.
Subject:   Linear algebra
Question:   Let vector v=[2,-1,1,3], x=[-1,2,-1,-1], y=[0,0,2,1], z=[1,1,2,3]

Are these vectors linearly independent?

If not, give one nontrivial solution of the corresponding system of linear equations,and write one dependency equation
..................................

No, they are not. If you form their matrix:

[2, -1, 1, 3]
[-1, 2,-1,-1]
[0,  0, 2, 1]
[1,  1, 2, 3]

and do Gauss row-reduction, you get something like this:

[1,  1, 2, 3]
[0,  1, 1, 1]
[0,  0, 2, 1]
[0,  0, 0, 0]

So take the third equation as:

2x3 + x4 = 0

and make  x4 the parameter.  Solve back for the others.
.....................................
Next time, tell me:

-- what do you know about the example?
-- what do your vocabulary terms mean?
-- what have you tried?

and I won't start to think you are just dumping your homework on us.

Volunteer

#### Paul Klarreich

##### Expertise

I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction. I can also try (but not guarantee) to answer questions on Abstract Algebra -- groups, rings, etc. and Analysis -- sequences, limits, continuity. I won't understand specialized engineering or business jargon.

##### Experience

I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.

Education/Credentials
-----------